x? + 4x for x < 4, x² + 2x – 8 log,(x + 5) for x24 Which of the following describes the domain of the piecewise function g(x) O(-c0, 2) U (2, 4) U (4, 0) O(-00, -4) U (-4, 2) U (2, c0) O (-00, 2) U (2, c0) O (-00, c0)

Q: Let f(x) = log₂ (x²+2x+1) and g(z) = log₂(x+1), find h(x) = f(x) + g(x). Oa) h(z) = 0 Ob) h(t) = 2 O…

A: This question can be solved using the concept of logarithmic function.

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

A:

Q: 3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a…

A: We want to find domain of g+f

Q: Show that f(x) = (3x - 2) / (5x - 3) , is its own inverse ?

A:

Q: 8) Find the inverse of the following function. f (x) = {(-3,6), (-2,5), (4, 2), (–4, 1), (5, – 5)}

A:

Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

A:

Q: 2. Which shows that f(x) = 5x² -2 and f-¹(x)=√√2 are inverse functions? O522 -2= *52…

A: If f(x) and f -1(x) are inverse functions then  (f∘f -1)(x)=(f -1∘f)(x)

Q: For the function given below, find its inverse from the 'procedural perspective' and graph the…

A:

Q: Consider the following function: 3x 10z - 17 1 - 10x -1 f(x) = 17 10 2 13 1 a) What is the highest…

A:

Q: a) x1+2log x = 100.x log x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Q5. Find z (1) 3 log, 2+log, 25-log, 20 = log (2) logą z + logs (2-3) = log, 10 (3) Inz-10.1285

A: As we know from the logarithmic properties: 1). logbxa=a·logbx  where x,b&gt;0, b≠1 2).…

Q: Assume you have functions f and g such that f(n) is O(g(n)). For each of the following statements,…

A:

Q: Evaluate (a) log(2-j3)(6(sin(√ī})² (b) 11/2

A: Given:  log2-j36sinj2 jjj2 To find: We have to evaluate the given expressions.

Q: x+7 22. (x)= 2x-7, gx) =; 2.

A:

Q: 6х + 11 The inverse function of f(x) = is ƒ-1(x) = %3D 9х + 10 о 11-10х 6+ 9x 11- 10х 9х — 6 о-11…

A: We find inverse of given function is

Q: Find the inverse function, g(y), of h(x) = √x+7. g(y) =

A: Given function is h(x)=x+74

Q: What happens to this base function that went from  a(x)= x2 to  h(x) = -x2+ 4 and why it happened?

A: The objective of the question is to understand the transformation of the base function a(x) = x^2 to…

Q: 19) Consider the function y = 5 log (z + 12) – 8. Complete the sentence about the graph of the…

A: Given that  Function y = 5log(x+12)-8

Q: Calculate by means of the logarithm: a) x¹+2log x= 100.x log x b) log(x+2)+log(x-7) = 2.log (x-4) c)…

A: We  have to calculate this equation by means of logarithm.Note: According to the guidelines we are…

Q: 6х + 11 The inverse function of f(x) = is f1(x) = Бл + 5 о 11-5z 6+ 5г -11 – 5z 6 — 5х о 11-5г 5л —…

A:

Q: 1. Find the inverse of the following functions and its domain and range. (9) x + 7 a)f(x) = - 8 - 5x…

A:

Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: 3) Calculate by means of the logarithm: a) x¹+2log x= 100.x log x b) log(x+2)+log(x-7) = 2.log (x-4)…

A:

Q: %3D What is the equation of the inverse of the function f(x) = log, (9x)? O A f-1 (x) = (2*) O B.…

A:

Q: find the inverse of the function f(x) = 2x +3/x-4

A: Given query is to find the inverse of f(x).

Q: Use composition to verity that f (2) = logi(z-5) and g (z) 3 +5 are inverses of each other. Show all…

A: f(x) and g(x) are inverse of each other if (fog)(x) = xand (gof)(x) = x

Q: [5] For each of the following functions f find a simple function g such that f(n) = (g(n)). (a)…

A: Given Data: We need to write Θ(g(n)) for given functions.

Q: 3. 9. a) Solve for x: log4 xX = b Write as a single log: 2log, 3x + 3log5y – 4log5z

A:

Q: find the inverse of f (x)=ax+b/cx-a

A:

Q: Which of the following gives the formula for the inverse of the function x + 3 f : R \ {-7/2} → R \…

A: I am attaching image so that you understand each and every step.

Q: Which of these functions is the inverse of f(x) = 4x - 1? O 1/(4x-1) O (1/4)x + (1/4) O (1/4)x -…

A: We have to find